# Conformal Vacuum and Fluctuation-Dissipation in de-Sitter Universe and Black Hole Spacetimes

## TL;DR

This paper investigates the behavior of quantum particles in curved spacetimes like de-Sitter and black hole backgrounds, showing that produced particles induce Brownian motion consistent with fluctuation-dissipation relations.

## Contribution

It demonstrates that in curved spacetimes, the correlation functions of particle fluctuations follow the fluctuation-dissipation theorem, linking quantum field effects to Brownian motion of test particles.

## Key findings

- Correlation functions obey fluctuation-dissipation theorem
- Test particles exhibit Brownian motion in quantum baths
- Particle production depends on observer's vacuum choice

## Abstract

In the studies of quantum field theory in curved spacetime, the ambiguous concept of vacuum state and the particle content is a long-standing debatable aspect. So far it is well known to us that in the background of the curved spacetime, some privileged class of observers detect particle production in the suitably chosen vacuum states of the quantum matter fields. In this work we aim to study the characteristics behaviour of these produced particles in the background of the de-Sitter (dS) Friedmann-Lama\^{i}tre-Robertson-Walker (FLRW) Universe (both for $(1+1)$ and $(3+1)$ dimensions) and $(1+1)$-dimensional Schwarzschild black hole (BH) spacetime, from the point of view of the respective privileged class of observers. Here the analysis is confined to the observers who perceive particle excitations in the conformal vacuum. We consider some test particles in the thermal bath of the produced particles and calculate the correlation function of the fluctuation of the random force as exerted by the produced quanta on the test particles. We obtain that the correlation function abides by the fluctuation-dissipation theorem, which in turn signifies that the test particles execute Brownian-like motion in the thermal bath of the produced quanta.